The two start-ups offer similar services, but they brand themselves differently. Uber markets itself as polished and professional, while Lyft presents a fun alternative: fuzzy pink mustaches are attached to its cars.

"Today, we still have a difference in terms of what these companies stand for, and who they go after," said Thilo Koslowski, an analyst at Gartner. "Lyft has a more social emphasis, where they want you to get to know people in that service. Uber is focused on getting you [to your destination] at a premium level."

The competition between has become one of the most hostile in Silicon Valley.

Uber's CEO Travis Kalanick took to Twitter to call Lyft a "clone," suggesting that his rival copied his service.

Zimmer disagrees. "We launched in 2012," he told CNBC. "There was no peer-to-peer or low-cost competitor. So we innovated in this space. Everything we have done is about building the right low-cost service. So others are following us. Those are the facts."